It seems likely that in the UK the Pressure Equipment Regulations (UK enactment of the Pressure Equipment Directive) would apply (if supplying these for beyond your own use).
The classification of the vessel described by the OP when used for compressed air would be 'Sound Engineering Practice' (the lowest category) – there is no specific requirement to involve any third party in review/witnessing of either design or manufacture/testing for SEP items.
There are requirements regarding marking, and provision of adequate instructions.
A Technical File should be prepared to cover the design, materials used, inspection & test – this would be a significant part of the manufacturer's defence if an incident did occur.
PED generally expects a pressure test, but does accept (justified) alternatives.
Don't forget to consider the potential for fatigue failure in this application.